63.5.2 problem 1(b)

Internal problem ID [13076]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.4.1. Integrating factors. Exercises page 41
Problem number : 1(b)
Date solved : Tuesday, January 28, 2025 at 04:51:31 AM
CAS classification : [_separable]

\begin{align*} \cos \left (t \right ) x^{\prime }-2 x \sin \left (x\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(cos(t)*diff(x(t),t)-2*x(t)*sin(x(t))=0,x(t), singsol=all)
 

\[ \ln \left (\sec \left (t \right )+\tan \left (t \right )\right )-\frac {\left (\int _{}^{x \left (t \right )}\frac {\csc \left (\textit {\_a} \right )}{\textit {\_a}}d \textit {\_a} \right )}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.282 (sec). Leaf size: 40

DSolve[Cos[t]*D[x[t],t]-2*x[t]*Sin[x[t]]==0,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\csc (K[1])}{K[1]}dK[1]\&\right ]\left [4 \text {arctanh}\left (\tan \left (\frac {t}{2}\right )\right )+c_1\right ] \\ x(t)\to 0 \\ \end{align*}